Firstly, get that thinking of your whole high school career riding on one project out of your head. It doesn't. That kind of thinking will just stress you out, and cloud your mind.

Secondly, what exactly do you mean by 'area'? Do you mean you're trying to maximize the amount of space on the ground that the tent occupies? If you could, please re-state the problem exactly as given. Is there another constraint (ie, does the tent need to fit -people- inside)?

Lastly, for a pup tent, your volume formula seems a little off. Have you drawn a picture? If you're having trouble, I would suggest first drawing a picture of an equilateral triangle (are you envisioning an equilateral triangle at each end of the tent)? Then two triangles connected in a tent fashion. What do you know about the height of an equilateral triangle, compared to the length of a side?

Edit: Volume formula probably fine, I was thinking of a different b (b = a/2 where a length of bottom)-- old habit I suppose.

As dotman said, it would have been helpful to say area of WHAT! You last equation doesn't help a lot. The 2 (1/2)bh terms are, of course, the area of the two ends. But 3(lb) is not any area of the tent.

I THINK you are trying to minimize the total area of the material used to make the tent. That includes the 2 ends as you have, the base (most put tents I have seen did NOT have a bottom, but okay) which would be lb, and the two "slant" sides- which are NOT "lb". The two slant sides each have area lc where c is the hypotenuse of the right triangle with legs of length h and b/2.